#### Transcript Ethics & Research

A short explanation of various statistical concepts Communication Research Week 9 Making the Case for Quantitative Research Advantages Tradition and history implies rigour Numbers and statistics allows precise and exact comparisons Generalisation of findings Limitations Cannot capture complexity of communication over time Difficult to apply outside of controlled environments 2 Basics of descriptive statistics Statisticians use mathematical methods to analyse, summarise and interpret data that have been collected The choice of statistical method of analysis depends on the data that have to be analysed (and the experience of the researcher) 3 Descriptive vs inferential statistics Descriptive statistics refer to methods used to obtain, from raw data, information that characterises or summarises just that set of data Inferential statistics allow us to generalise from the data collected to the general population they were taken from 4 Different statistical measures Raw data is unorganised but can be tabulated to make it easier to understand and to interpret It is usually presented as a frequency table or graph A frequency chart will allow a researcher to see trends or groupings of data and how they are distributed 5 Characteristics of each distribution Location – where on the axis is the distribution positioned? Dispersion – how broad is the distribution? Shape – what is the form (appearance, pattern) of the distribution? The type of data you have to analyse will determine the statistical measure chosen Statistics describing the location of the distribution are called measures of central tendency 6 Measures of central tendency – the mean The mean is the sum of all observed data values divided by the sample size (the arithmetic average) Describing data that are interval or ratio in nature (eg speed of response, age in years) calls for the mean One of the main disadvantages is that it is most profoundly affected by extreme scores 7 Calculating a Mean Score Scores: 79 81 82 86 86 88 91 93 95 97 total = 878 Divide by n = 10 scores Mean = 87.8 8 Measures of central tendency – the median The median is the score or the point of distribution above which one half of the scores lie eg in a simple set of scores such as 1, 3, & 5 the median is 3 The median is best suited to data that are ordinal or ranked ( eg birth order, rank in class) To compute the median Order the scores from lowest to highest Count the number of scores Select the middle score When the number of scores is even, find the mean of the two middle scores eg 31 33 35 38 40 41 42 43 44 46 47 48 49 50 N = 14 (no of scores); Median = (42 + 43) ÷ 2 = 42.5 9 Two distributions of scores Distribution 1 Distribution 2 24 24 25 25 26 26 Mean = 25 Range = 3 16 19 22 25 28 30 35 Mean = 25 Range = 20 10 Measures of central tendency – the mode The mode is the most frequently observed value in the frequency distribution ie it is the score that occurs most frequently The mode is best used for nominal data and for data that are qualitative in nature such as gender, eye colour, ethnicity, school or group membership In the following list of numbers: 58 27 24 41 27 26 41 53 24 29 41 53 47 28 56 The mode is 41 because it occurs 3 times A common mistake is to identify the mode as how frequently the value occurs (3) not the value itself (41) 11 Which measure when? Which measure of central tendency? Measure Level of measurement Examples Mode Nominal or categorical – ie qualitative Median Ordinal or ranked Rank in class, birth order Mean Interval and ratio Speed of response, age in years Gender, hair or eye colour, group membership, ethnicity, school etc 12 Three Measures of Variability Range: the difference between the highest and lowest scores in a distribution of scores. Variance: a measure of dispersion indicating the degree to which scores cluster around the mean score. Standard deviation: index of the amount of variation in a distribution of scores. 13 Standard deviation SD is a measure of the variability indicating the degree to which all observed values deviate from the mean SD can only be used for interval and ratio data, not nominal data (eg gender) It is the most frequently used statistic as a measure of dispersion or variability The larger the SD, the more variable the set of scores is 14 COMPUTING DEVIATION SCORES Raw Mean DEV. SQUARED score score deviation score 4 - 10 = -6 36 8 - 10 = -2 4 9 - 10 = -1 1 10 - 10 = 0 0 10 - 10 = 0 0 10 - 10 = 0 0 12 - 10 = 2 4 13 - 10 = 3 9 14 - 10 = 4 16 90/9 = 10.00 = MEAN 70/9 = 7.77 = Variance STANDARD DEVIATION: (Square Root of Variance) = 2.79 15 Types of Variables Variable Element that is identified in the hypothesis or research question Property or characteristic of people or things that varies in quality or magnitude Must have two or more levels Must be identified as independent or dependent 16 Independent Variables Manipulation or variation of this variable is the cause of change in other variables (the cause) Technically, independent variable is the term reserved for experimental studies Also called antecedent variable, experimental variable, treatment variable, causal variable, predictor variable 17 Dependent Variables The variable of primary interest that is measured (the effect) Research question/hypothesis describes, explains, or predicts changes in it The variable that is influenced or changed by the independent variable In non-experimental research, also called criterion variable, outcome variable 18 Relationship Between Independent and Dependent Variables Cannot specify independent variables without specifying dependent variables Number of independent and dependent variables depends on the nature and complexity of the study The number and type of variables dictates which statistical test will be used 19 Issues of Reliability and Validity Reliability = consistency in procedures and in reactions of participants Validity = truth - Does it measure what it intended to measure? When reliability and validity are achieved, data are free from systematic errors 20 Threats to Reliability and Validity If measuring device cannot make fine distinctions If measuring device cannot capture people/things that differ When attempting to measure something irrelevant or unknown to respondent Can measuring device really capture the phenomenon? 21 Other Sources of Variation Variation must represent true differences Other sources of variation Factors not measured Personal factors Differences in situational factors Differences in research administration Number of items measured Unclear measuring device Mechanical or procedural issues Statistical processing of data 22